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% Example to illustrate security strategies
%
% Author: K. Passino
% Version: 1/22/02
%
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clear all

% Set the number of different possible values of the decision variables

m=5; % If change will need to modify specific J1 value chosen below
n=3; 

% Set the payoff matrix J1(i,j):

%J1=round(10*rand(m,n)-5*ones(m,n)); % Make it random integers between -5 and +5

J1 =[-3     4     4; % Just saved this from the screen for one case to get consistent values
     0    -5     2;  % (comment this J1 out to get random payoff matrices, or to change n, m)
     -2    1    -4;
     2     3    -4;
     2    -2    -5]

% Compute the security strategy and value for each player, P1 then P2

[maxvals,indexmax]=max(J1'); % This is the max value for each row (note transpose)
maxvals' % Display the max values of each row

[secvalP1,secstratP1]=min(maxvals) % Display the security value of P1 and its security strategy


[minvals,indexmin]=min(J1); % This is the min value for each column (note no transpose)
minvals % Display the min values of each column

[secvalP2,secstratP2]=max(minvals) % Display the security value of P2 and its security strategy

% The outcome of the game will be

gameoutcome=J1(secstratP1,secstratP2)


% Plot the payoff values (clearly can just read the security value and strategy directly off 
% this plot by inspection)

figure(1)
clf
subplot(211)
bar(1:m,J1)
grid
xlabel('Decision of player 1, i')
title('(a) J^1(i,j), groups are payoffs for j=1,2,...,n')
subplot(212)
bar(1:n,J1')
grid
xlabel('Decision of player 2, j')
title('(b) J^1(i,j), groups are payoffs for i=1,2,...,m')


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% End of program
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